Why is laughing gas used when having wisdom teeth pulled?

Your comfort. Nitrous can help some patients feel more relaxed during the procedure. You will still have local anesthesia (injections) administered.
Relaxation. Laughing gas or nitrous oxide gas is used to put the patient at ease so that the wisdom teeth procedure will appear quicker and smooth. Another option to consider that most patients like is IV sedation. Patients often don't remember anything and it is even quicker and easier. See an oral surgeon for a consultation.
Anxiety. Most people are very nervous about having their wisdom teeth pulled. The laughing gas helps to relieve some of that nervousness.
Minimize anxiety. Laughing gas does not make you sleepy but can minimize anxiety during the procedure. Local anesthesia is still required. Make sure you go to a doctor trained in administering anesthesia.